相关论文: Resonant phenomena in slowly perturbed elliptic bi…

We extended a previous qualitative study of the intermittent behaviour of a chaotical nucleonic system, by adding a few quantitative analyses: of the configuration and kinetic energy spaces, power spectra, Shannon entropies, and Lyapunov…

We discover that the energy-integral of time-delay is an adiabatic invariant in quantum scattering theory and corresponds classically to the phase space volume. The integral thus found provides a quantization condition for resonances,…

We study the convergence towards the equilibrium for a dissipative and stochastic time-dependent oval billiard. The dynamics of the system is described by using a generic four dimensional nonlinear map for the variables: the angular…

In standard (mathematical) billiards a point particle moves uniformly in a billiard table with elastic reflections off the boundary. We show that in transition from mathematical billiards to physical billiards, where a finite size hard…

Can elliptic islands contribute to sustained energy growth as parameters of a Hamiltonian system slowly vary with time? In this paper we show that a mushroom billiard with a periodically oscillating boundary accelerates the particle inside…

The coherent tunneling phenomenon is investigated in rectangular billiards divided into two domains by a classically unclimbable potential barrier. We show that by placing a pointlike scatterer inside the billiard, we can control the…

Starting with a post-Newtonian description of compact binary systems, we derive a set of equations that describes the evolution of the orbital angular momentum and both spin vectors during inspiral. We find regions of phase space that…

In this work we study the nonlinear dynamics of the static and the driven ellipse. In the static case, we find numerically an asymptotical algebraic decay for the escape of an ensemble of non-interacting particles through a small hole due…

We propose geometric tools that are suitable for studying the behavior of a billiard trajectory in a homogeneous force field. Two examples are considered: a vertical plane with an open top and with a parabolic or right angle boundary at the…

A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the…

What we are going to call in this paper "diffractive phenomena" in billiards is far from being deeply understood. These are sorts of singularities that, for example, some kind of corners introduce in the energy eigenfunctions. In this paper…

Given a random map (T_1, T_2, T_3, T_4, p_1, p_2, p_3, p_4), we define a random billiard map on a surface of constant curvature (Euclidean plane, hyperbolic plane, or the sphere). The Liouville measure is invariant for this billiard map.…

Introducing the rotor interaction in the integrable system of the annulus billiard produces a variety of dynamical phenomena, from integrability to ergodicity.

We investigate the dynamics of a soliton that behaves as an extended particle. The soliton motion in an effective bistable potential can be chaotic in a similar way as the Duffing oscillator. We generalize the concept of geometrical…

The billiard problem concerns a point particle moving freely in a region of the horizontal plane bounded by a closed curve $\Gamma$, and reflected at each impact with $\Gamma$. The region is called a `billiard', and the reflections are…

We study dynamics of a nonlinear pendulum under a periodic force with small amplitude and slowly decreasing frequency. It is well known that when the frequency of the external force passes through the value of the frequency of the…

While billiard systems of various shapes have been used as paradigmatic model systems in the fields of nonlinear dynamics and quantum chaos, few studies have investigated anisotropic billiards. Motivated by the tremendous advances in using…

Non-linear parametric resonances occur frequently in nature. Here we summarize how they can be studied by means of perturbative methods. We show in particular how resonances can affect the motion of a test particle orbiting in the vicinity…

Some of the subtleties of the integrability of the elliptic quantum billiard are discussed. A well known classical constant of the motion has in the quantum case an ill-defined commutator with the Hamiltonian. It is shown how this problem…

This paper explores two instances where dissipation plays a crucial role in curbing the unbounded energy growth of particles in time-dependent billiards. The first example involves an elliptical-like billiard with inelastic collisions…